Question

question 8 (3 points) find m∠1, m∠2 and m∠3. complete the reasoning. m∠1 = 47 ° and ∠3 are angles. m∠2 = 133 ° and the given are alternate interior angles m∠3 = 47 ° and ∠2 are supplementary angles blank 1: 47 blank 2: blank 3: 133 blank 4: alternate interior blank 5: 47 blank 6: supplementary

Explanation:

Step1: Identify vertical - angle relationship

$\angle1$ and $\angle3$ are vertical angles. Vertical angles are congruent. Given $\angle1 = 47^{\circ}$, so $\angle3=47^{\circ}$.

Step2: Identify alternate - interior angle relationship

$\angle2$ and the given $133^{\circ}$ angle are alternate - interior angles. Alternate - interior angles are congruent when the lines are parallel. So $m\angle2 = 133^{\circ}$.

Step3: Identify supplementary - angle relationship

$\angle2$ and $\angle3$ are supplementary angles (since $\angle2+\angle3 = 133^{\circ}+47^{\circ}=180^{\circ}$).

Answer:

Blank 1: 47
Blank 2: vertical
Blank 3: 133
Blank 4: alternate interior
Blank 5: 47
Blank 6: supplementary